Problem: Simplify the following expression: $\dfrac{8p^5}{14p^2}$ You can assume $p \neq 0$.
Explanation: $ \dfrac{8p^5}{14p^2} = \dfrac{8}{14} \cdot \dfrac{p^5}{p^2} $ To simplify $\frac{8}{14}$ , find the greatest common factor (GCD) of $8$ and $14$ $8 = 2 \cdot 2 \cdot 2$ $14 = 2 \cdot 7$ $ \mbox{GCD}(8, 14) = 2 $ $ \dfrac{8}{14} \cdot \dfrac{p^5}{p^2} = \dfrac{2 \cdot 4}{2 \cdot 7} \cdot \dfrac{p^5}{p^2} $ $\phantom{ \dfrac{8}{14} \cdot \dfrac{5}{2}} = \dfrac{4}{7} \cdot \dfrac{p^5}{p^2} $ $ \dfrac{p^5}{p^2} = \dfrac{p \cdot p \cdot p \cdot p \cdot p}{p \cdot p} = p^3 $ $ \dfrac{4}{7} \cdot p^3 = \dfrac{4p^3}{7} $